I was in the same boat as you, Noah: stiff as a board, and I had very short, tight muscles and ligaments. While doing frontbends I could barely touch mid-shin, and my shoulders had limited range of motion. This lack of flexibility resulted in my acquiring a slew of over-use injuries from my training, in aikido, running, and bodyweight exercises: i developed plantar fasciitis and achilles tendonitis, always had stiff hips, and had chronic neck stiffness.

I started doing yoga consistently: first a one hour class two times a week, then as I got more experienced and comfortable (probably 3 months) I started going to class 4 times a week, then i started doing yoga on my own (once my instructor felt my form was correct) every day before I went to bed. I didn't do it for long: maybe 20 minutes or so, but I did it every day, just a little bit, and this was when I started having the most improvement.

Now after about a year, without much effort i can bend over and put my entire palm on the floor. I can do a backbend now (though its very ugly). I rarely get injuries anymore.

How has this translated into my aikido? Well, I've noticed it takes people a lot more effort to get me to tap out when they pin me, especially the sankyo and nikkyo ground pins. I love those pins because they help me stretch out my shoulder even more. Most joint lock techniques don't quite have much oomph to me anymore, which makes me a better uke: I don't fall just because of application of pain anymore, the nage really has to lock out my musculature and take my balance to get me down.

But the key to all this was steady, consistent progression, pushing yourself just a little bit each week, and listening to your body.

Good luck!

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train as if the tengu will never visit, execute as if they already have